Recently, our understanding of global symmetries has undergone
something of a renaissance. The idea that the existence of conserved
quantities can be recast in terms of the topological surface operators
who count the charge has led to powerful generalizations of the very
concept of “symmetry”. Two such generalizations which will concern
us in this paper are those of higher-form symmetries – i.e. the
symmetries associated with the conservation of extended objects
[1]} – and non-invertible symmetries,
i.e. symmetries for which the charges do not obey a simple group
composition law
[2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}, [11]}, [12]}, [13]}, [14]}, [15]}, [16]}, [17]}, [18]}, [19]}, [20]}, [21]}, [22]}, [23]}, [24]}, [25]}, [26]}, [27]}, [28]}, [29]}, [30]}, [31]}, [32]}, [33]}, [34]}. See
e.g. [35]} for a recent pedagogical review of some
of these developments.
